## Subglacial Water Pressure

4.6.1 Subglacial Water Pressure and Effective Normal Pressure

Subglacial water pressure has an important role in many subglacial processes, through its control on the effective normal pressure beneath a glacier. Effective normal pressure is the force per unit area imposed vertically by a glacier on its bed. For a cold-based glacier it is effectively equal to the weight of the overlying ice; thick ice imposes a greater pressure than thin ice. This is summarised by:

N = pgh where N is the normal effective pressure, p is the density of ice, g is acceleration due to gravity and h is ice thickness.

If water is present at the glacier bed, however, the effective normal pressure is reduced by an amount equal to the subglacial water pressure. Put crudely, the greater the water pressure the more it can support the weight of the glacier and thereby reduce the effective normal pressure acting on the bed. The equation is modified to:

N = pgh — wp where N is the normal effective pressure, p is the density of ice, g is acceleration due to gravity, h is ice thickness and wp is the subglacial water pressure.

This is only true where the glacier has a flat bed. Effective normal pressure is modified by the flow of ice over obstacles (Figure 4.6). As ice flows against the upstream side of an obstacle the effective normal pressure increases by an amount proportional to the rate of glacier flow against the obstacle. Effective normal pressure is also reduced in the lee or on the downstream side of the obstacle (Figure 4.6). The pressure fluctuation caused by the flow of ice against the obstacle is, therefore, positive on the upstream side and negative on the downstream side. The negative pressure fluctuation on the downstream side of an obstacle may cause

Figure 4.6 Schematic diagram of the distribution of effective normal pressure at the glacier bed as it flows over a bedrock obstacle. [Modified from: Boulton (1974), in Glacial Geomorphology (ed. Coates), George Allen and Unwin, figure 8, p. 55]

a cavity to form in its lee if the effective normal pressure at this point is exceeded (Figure 4.7). Cavity formation is favoured by: (i) thin ice (ii) high basal water pressures, which reduce effective normal pressure; and (iii) high rates of basal sliding, which produce large pressure fluctuations over obstacles. Theoretical calculations show that cavities can open at sliding velocities of about 9 m per year beneath a thickness of 100 m of ice, whereas velocities of 35 m per year are required with ice thickness of the order of 400 m.

Basal water pressure is controlled by four variables: (i) glacier thickness - the greater the weight of the overlying ice the greater the water pressure; (ii) the rate of water supply - the input of large amounts of meltwater may increase the pressure; (iii) the rate of meltwater discharge - an efficient subglacial drainage system will reduce water pressure; and (iv) the nature of the underlying geology - permeable bedrock, for example, will reduce water pressure. Variations in the rate of water supply and the rate of meltwater discharge are responsible for much of the seasonal variation in water pressure present at some glaciers. Early in the melt season water pressure may be very high due to the abundance of meltwater and the relative inefficiency of the channel network (see Section 4.7). As the subglacial channel network develops during the ablation season discharge becomes more efficient and the water pressure generally falls.

As we will see in Chapters 5 and 6, variations in water pressure and its influence on effective normal pressure and cavity formation are very important for the processes of glacial erosion. Basal water pressure is also important in determining the rate of basal sliding (see Section 3.3.2). Effective normal pressure helps determine the friction experienced between a glacier and its bed. If the water pressure

Ice veiocit

### Ice veiocit

Figure 4.6 Schematic diagram of the distribution of effective normal pressure at the glacier bed as it flows over a bedrock obstacle. [Modified from: Boulton (1974), in Glacial Geomorphology (ed. Coates), George Allen and Unwin, figure 8, p. 55] Figure 4.7 Photograph of a large subglacial cavity in the lee of a rock step beneath the southern margin of San Rafael Glacier in Chile. Ice flow is from right to left over the rock step.

[Photograph: N. F. Glasser]

Figure 4.7 Photograph of a large subglacial cavity in the lee of a rock step beneath the southern margin of San Rafael Glacier in Chile. Ice flow is from right to left over the rock step.

[Photograph: N. F. Glasser]

rises, effective normal pressure will fall, thereby reducing basal friction and consequently increasing basal sliding. This explains why sliding velocity often increases during the summer melt season or after a large rainfall event. For example, field observations on the Unteraargletscher have shown that it moves vertically by 0.4 m at the start of the melt season due to increased water pressure. This is followed by a similar downward movement at a constant rate over the next 3 months. The glacier velocity increases significantly when the surface is raised. Variations in basal water pressure have also been linked to glacier surges. For example, the surge of the Variegated Glacier in Alaska, during 1982-1983 is believed to have been triggered by a change in the subglacial drainage system. Prior to the surge the glacier had a subglacial drainage system dominated by a few large tunnels. This appears, however, to have changed to a system dominated by linked subglacial cavities in which the water pressure rose dramatically due to the lower rate of discharge possible from such a system. This rise in water pressure facilitating rapid glacier flow during the surge, but at the end of the surge this stored water was released as a large flood and the subglacial system reverted to a large integrated tunnel system. The cause of this change in drainage system is unclear, but is believed to be central to the rapid glacier flow of this surge.

In summary therefore variation in basal water pressure has an important role to play in determining the flow dynamics of a glacier and is also important in the processes of glacial erosion (see Chapter 5).

4.6 Subglacial Water Pressure 93 4.6.2 Water Pressure Gradients

The orientation of this network of conduits and tunnels is controlled by the water pressure gradient within the glacier. Water will flow down the pressure gradient from areas of high to low pressure. It is possible to determine the nature of this pressure gradient within a glacier and therefore the direction of water flow within it. Figure 4.8 shows a hypothetical water-filled tube beneath a glacier. The weight of ice above point A is equal to the weight of the water column B-C which it forces up. A line between A and C defines a surface of equal potential pressure. Along this line the pressure due to the weight of the overlying ice is equal to the water pressure it generates. If we now move the tube towards the right, closer to the ice margin, the Figure 4.8 Diagram to illustrate the hydraulic head which drives water flow within a glacier. The weight of the ice above point A is equal to the elevation of the water column BC. The thinner the ice above point A, the less the hydraulic head. Consequently the hydraulic head or potential will fall towards the ice margin or in the direction of glacier slope. Water flows from areas of high hydraulic potential to areas of low hydraulic potential.

Figure 4.8 Diagram to illustrate the hydraulic head which drives water flow within a glacier. The weight of the ice above point A is equal to the elevation of the water column BC. The thinner the ice above point A, the less the hydraulic head. Consequently the hydraulic head or potential will fall towards the ice margin or in the direction of glacier slope. Water flows from areas of high hydraulic potential to areas of low hydraulic potential.

weight of the ice above point A will fall and consequently the water column B-C will be lower. A new lower equipotential surface is defined. Water will flow at right angles to these equipotential surfaces from a surface of higher potential pressure to one of lower potential pressure. As a consequence englacial conduits and tunnels will be orientated perpendicular to surfaces of equipotential pressure (Figure 4.9). Some moulins may be an exception to this, reflecting their origin as crevasses. The geometry of the equipotential surfaces within a glacier is determined by the variation in ice thickness, which is controlled primarily by the surface slope of the glacier and secondarily by the slope of the underlying topography. The surface of a glacier does not always slope in sympathy with the slope of the glacier bed. As a consequence subglacial meltwater may not always flow directly down the maximum slope beneath the glacier and may in some cases even flow uphill. Under an ice sheet water flow will be approximately radial, in sympathy with the surface slope and the direction of ice flow, but will deviate around hills and bumps and be concentrated in topographic depressions such as valleys.

It is possible to calculate the water pressure potential at a series of points at the base of a glacier from knowledge of the variation in ice thickness. These points can be contoured to define a surface known as the subglacial hydraulic potential surface (Figure 4.9). Provided that any subglacial tunnel is completely water filled then the tunnel should be orientated at right angles to this hydraulic surface. The ability to calculate this surface is a useful tool in the Figure 4.9 The pattern of equipotential surfaces within a glacier (i.e. surfaces of equal hydraulic potential). Water will always flow from areas of high hydraulic potential to areas of low hydraulic potential, and therefore it will flow at right angles to the equipotential surfaces as depicted here.

Figure 4.9 The pattern of equipotential surfaces within a glacier (i.e. surfaces of equal hydraulic potential). Water will always flow from areas of high hydraulic potential to areas of low hydraulic potential, and therefore it will flow at right angles to the equipotential surfaces as depicted here.

interpretation of the glacial landform record (Box 4.2). If the subglacial tunnel is not, however, completely full of water, something which may occur at the ice margin, then the water flow and the orientation of the tunnel may be controlled by the underlying topography beneath the glacier and not by the subglacial water pressure surface. The presence of gravity driven subglacial flow at the margin of glaciers has been investigated using dye-tracing experiments (Box 4.3). This technique can also be used to understand the seasonal evolution of subglacial drainage systems (Box 4.4).